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# find the equation to the locus of a point which moves so that its distance from the axis of X is always one half its distance from the origin

Arun
25763 Points
3 years ago
Dear Kamal

Let the point = (x, y)
Hence its distance from X -axis = y

Now
Its distance from origin = $\sqrt$(x² +y²)

Hence
(1/2)$\sqrt$x²+y² = y
On squaring
(1/4)(x² +y²) = y²
x² = 3y²

Regards